THE ANNOUNCEMENT that the missionaries of the Charity of Calcutta plan to open a house of prayer in Washington at first prompts not just gratitude by also puzzlement. The gratitude, obviously, is for the interest that Mother Teresa, leader of the mission and winner of the 1979 Nobel Peace Prize, is showing in this city and its poor. To gain her attention and to be part of her mission is no small blessing. The puzzlement concerns why Mother Teresa would pick this city, which is far from being a poor American city and certainly no equal of the world where she has served. It was in the slums of Calcutta that Mother Teresa tended to the destitute, to lepers and beggars for over 30 years. Her work there won her the peace prize and worldwide acclaim.

The answer has to do with larger intentions. Since winning the prize, Mother Teresa has opened about 20 homes a year around the world. In this country, she has established homes in the South Bronx, in Los Angeles, in St. Louis and in Detroit. In those cities, the work of her houses of prayer has been mission-like: spreading the word of Christ through poor areas, visiting prisoners and helping the hungry and homeless. There are also homes in some of those cities for prayer alone -- nuns praying 12 hours a day -- and such a home will be established here in Washington. The working component of the group's Washington home, to be located in Southeast, will be four nuns who go into the community daily and try to help people "accept their situation, expose them to the ministry of Christ and serve where possible," in the words of a spokesman for the Catholic archdiocese of Washington. It was Archbishop James Hickey who invited Mother Teresa to bring her charity mission here.

There will also be a third part to the charity's Washington group: a center for religious retreats and religious education. This is meant to serve as a possible gathering place in the nation's capital for people interested in Mother Teresa's work. That could be the most important part of her mission in Washington, a natural crossroad for world leaders and activists. However, no definite plans have been made about the size or activities of Mother Teresa's homes in Washington, and changes are possible, such as increasing the number of nuns permanently assigned here. As it is now conceived, though, Mother Teresa's work in Washington will be mostly educational and an effort to develop good will for her worldwide missions. An example of that sort of work was her testimony last week at Capitol Hill symposium against abortion. She advocates greater reliance on adoption.

While Washington is certainly rich by world standards, Mother Teresa's nuns will find that there is some poverty here in American terms, particularly in the Southeast area where the home will be located. The problems have to do with housing, with poor education and with drug use. These difficulties are especially hard for young blacks, a large number of whom are unemployed despite the great wealth of other sections of this city. This is the terrain that Mother Teresa's charity will have to work on in Washington. She and her mission are to be welcomed as much for what effort they make with Southeast's troubles as for the education and lobbying for the poor they will do here.